Dimensionality determination: A thresholding double ridge ratio approach

Xuehu Zhu, Xu Guo, Tao Wang, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


Underdetermination of model dimensionality (order) is a longstanding problem when existing eigendecomposition-based criteria are used. To alleviate this difficulty, we propose a thresholding double ridge ratio criterion in this paper. Unlike all existing eigendecomposition-based criteria, the proposed criterion can provide a consistent estimate even when there are several local minima. For illustration, we present the generic strategy with three important applications: dimension reduction in regressions with fixed and divergent dimensions; model checking with local alternative models; and ultra-high dimensional approximate factor models. Numerical studies are conducted to examine the finite sample performance of the proposed method and a real data example is analyzed for illustration.

Original languageEnglish
Article number106910
Number of pages18
JournalComputational Statistics and Data Analysis
Publication statusPublished - Jun 2020

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Double ridge ratio criterion
  • Factor models
  • Local regression models
  • Sufficient dimension reduction
  • Thresholding


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